Pilot and laboratory test procedures for the design of

PILOT AND LABORATORY TEST PROCEDURES 1

IntroductionThe attractive feature of semi-autogenous grinding mills isthat they can be fed directly with coarse ROM (run of mine)ore with 80 per cent passing sizes often in excess of150 mm. This obviates the need for complex multi-stagecrushing and screening plants prior to milling, although aprimary crusher and grizzly is often needed to constrain thefeed to a top size that can easily be handled and transportedto the mill. Large rocks in the ROM ore serve as grindingmedia that can self-break and also break ore in intermediateand fine sizes. For some ores, effective grinding can occurwithout the need for steel grinding balls (sometimesreferred to as AG or autogenous grinding). However, ballsare often added to prevent the build-up of so called criticalsizes that do not easily self-break and cannot be efficientlybroken down by the largest rocks in the mill. The bulkvolume of the balls added is typically a few per cent of theinternal mill volume (hence the term SAG or semi-autogenous grinding), but can be as high as thirty per cent.SAG mills with very high ball loads are not uncommon insome South African precious metal operations and are

usually referred to as ROM ball mills. Although semi-autogenous grinding appears to be a very

simple way of achieving large size reduction ratios in asingle unit, the design, control, and optimization of grindingcircuits incorporating SAG mills are not trivial tasks. Oneapproach is to conduct tests at pilot scale using ROM orewith the same size distribution and composition as the orelikely to be encountered at production scale. Based onpiloting tests conducted at Mintek over three decades, it hasbeen found that data generated from a SAG mill with aninternal diameter of 1.7 m can provide a good indication ofthe performance of production mills (Loveday,1978). Otherworkers hold similar views (Mosher and Bigg, 2002).

For pilot mills with internal diameters close to 1.7 m, thenet specific energy remains essentially invariant to scale-upfor a given circuit configuration and grind size. However,there are limitations with regard to the size of the largestrocks that can be handled (250 mm for the Mintek mill).Moreover, some corrections must be made to allow fordifferences in the grate geometry and aspect ratio of the testpilot mill and the production mill. Obviously, even at pilot

HINDE, A.L. and KALALA, J.T. Pilot and laboratory test procedures for the design of semi-autogenous grinding circuits treating platinum ores. ThirdInternational Platinum Conference ‘Platinum in Transformation’, The Southern African Institute of Mining and Metallurgy, 2008.

Pilot and laboratory test procedures for the design of semi-autogenous grinding circuits treating platinum ores

A.L. HINDE and J.T. KALALA Mintek

Mintek has been actively involved for many years in research aiming to improve piloting, plantsurvey techniques, laboratory test procedures and reliable models for the design of autogenous andsemi-autogenous tumbling mills.

Semi-autogenous piloting facilities and procedures used at Mintek are reviewed in this paper. Anovel laboratory test developed by Mintek to design semi-autogenous and autogenous millingcircuits based on fundamental principles rather than relying on empirical relationships is alsopresented. Results obtained from the novel test are compared to piloting results using a UG2 ore.

The steady-state and dynamic behaviour of semi-autogenous grinding (SAG) mills are arguablybest described using a population model that caters for the breakage kinetics and the materialtransport of rock and pulp inside the mill. Breakage kinetics are usually expressed in terms of aspecific breakage rate function and a separate primary breakage distribution function. Materialtransport usually invokes the concept of a specific discharge rate function. Unfortunately, thebreakage rate and breakage distribution functions for SAG mills are very difficult to estimateuniquely from plant data alone. Simplifying assumptions must be made to overcome this problem,which leads to many unresolved dilemmas with regard to whether or not the derived functions areaccurate, precise, and reflect reality. It is shown in this paper that the dilemmas associated withstandard population balance models (models that utilize separate breakage rate and breakagedistribution functions) can be overcome by expressing breakage behaviour inside a SAG mill interms of a single function. This function is an energy-based cumulative breakage rate functiondefined as the fractional rate at which particles and rocks coarser than a given size break to belowthat size per unit specific energy input. A model for SAG milling is formulated, which invokes theconcept of a cumulative breakage rate function. Comparisons are made between the mathematicalstructure of this “simple model” and standard population balance models.

It is concluded that the novel laboratory test developed by Mintek which has been filed for apatent is accurate and reliable. The simplified approach to model SAG milling may turn out to bethe quickest way to fully describe and quantify the performance of these very complex mills.

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PLATINUM IN TRANSFORMATION2

scale it is a costly exercise to explore all grate/linergeometries, operating conditions, and circuit configurationsto establish optimal design parameters. Accordingly, thereis considerable incentive to develop mathematical modelsthat can be used to accurately extrapolate and interpolatepilot and production data using computer simulationtechniques.

Consideration is first given to the use of ‘standard’population balance models (models that incorporateseparate specific breakage rate and breakage distributionfunctions) currently available for quantifying the behaviourof SAG mills. It is shown that whilst these models havemany attractive features, the functions used to modelbreakage kinetics and material transport can be verydifficult to quantify and give rise to many unresolveddilemmas. It is argued that these dilemmas can be resolvedby using functions to model breakage kinetics and materialtransport that can be measured directly from pilot SAGmills without having to make any a priori assumptionsabout their mathematical structure. Consideration is thengiven to the formulation of a simple model for SAG millingbased on these directly measurable functions.

Although piloting tests are the most reliable method forthe design of AG/SAG milling circuits, the cost associatedwith the test is very high and sometimes the amount of orerequired for the test, which is around 90 t, is not available,depending on the stage of the project. Over the past years,several bench-scale laboratory test procedures have beenused to design AG/SAG mills. A comprehensive review ofbench-scale testwork available was conducted at the 2006Autogenous and Semiautogenous grinding conference inCanada (McKen, A. and Williams, S., 2006). Recently(Hinde, A.L. and Kalala, J. T., 2007), Mintek has developeda bench-scale test procedures based on fundamentalprinciples rather than relying on empirical relationships.Results obtained from the novel test are compared topiloting results for a developed UG2 platinum ore.

Mintek SAG piloting facilityMintek comminution piloting facility includes a SAG mill,crushers, a Koppern High Pressure Grinding Roll (HPGR)unit having a diameter of 1 m, a Polysius unit having adiameter of 0.250 m, secondary ball mills, a stirred mediadetractor (SMD), a Deswik mill, a Derrick screen andhydrocyclones.

The SAG mill has an inside diameter of 1.7 m and aneffective length of 0.5 m. The mill operates at 75 per cent

of critical speed. It is equipped with six peripheral ports(each 75 mm by 175 mm). Each peripheral port canaccommodate a range of grate discharge and pebble portgeometry.

To control the feed rate to the mill, Mintek pilotingsystem is equipped with the sophisticated StarCS software.The StarCS software provides an automated control of thefeed particle size distribution to the mill. The system usedat Mintek involves the manual addition of individual rocksin the size classes coarser than 106 mm on the mainconveyor to the mill at timed intervals. The inclinedconveyor is connected to a weightometer from which thetotal solids feed rate is obtained. Known masses of rocks inthe size classes of typically –106 + 50 mm, -150 + 106 mmand –212 + 150 mm are loaded into buckets. The contentsof the buckets are placed at timed intervals on a slow-moving conveyor which discharges onto the mainconveyor. At Mintek, this system is computerized to cue theoperators (by switching on lights) when to load the rocksand which size class must be added (Figure 1).

The mill power draw is recorded by measuring the torqueusing a strain gauge on the pinion shaft and by monitoringthe motor energy consumption (using a kilowatt-hourmeter). The net power is given by the difference betweenthe gross power and the power to overcome drive losses(no-load power).

The mill power and grinding efficiency is affected by theslurry hold-up. The slurry hold-up can be changed during acampaign by increasing or decreasing the total gratedischarge opening area. Figure 2 shows an example of adischarge grate used in the pilot mill and Figure 3 showsmodifications which can be performed to increase ordecrease the total open area.

The hold-up mass of the charge is continuouslymonitored via four load cells mounted on the mill and drivesystem. The load cells determine the variation of the totalmass of the load to an accuracy of about 2 kg.

Standard SAG models

Basic conceptsThe state of the ore charge inside a SAG mill can becharacterized by the mass and particle size distribution ofeach rock-type. Usually, the particle size distribution isexpressed as the discrete mass fractions retained on sieves

Figure 1. Mintek SAG piloting facility Figure 2. Example of grate discharge used in the pilot mill



with mesh sizes conforming to a root-two geometricprogression. Breakage phenomena causing changes in thestate of the ore charge are usually expressed in terms of aspecific breakage rate function and a primary breakagedistribution function.

The specific breakage rate function, Si,k [h]-1 is defined asthe fractional rate at which particles of a given rock type(indexed by the subscript k) break out of a given size class(indexed by the subscript i) per unit time. It is usuallydesirable to transform the specific breakage function ratefunction from the time domain to an energy-based domain.This is motivated by the fact that grind size is more closelyrelated to specific energy input, rather than residence time.According to the Herbst Fuerstenau transformation (Herbstand Fuerstenau, 1980), the energy-based breakage ratefunction, SE

i,k [kWh/t]-1 can be defined by:

[1]

whereP is the mill net power, [kW]D is the internal diameter of the mill, [m]L is the effective mill length, [m]M is the ore holdup mass, [t]The utility of using an energy-based specific breakage

rate function is that it is insensitive to scale-up, whereas atime-based specific breakage rate function increases withmill diameter. This should be self-evident from Equation[1] since:

In other words, a time-based breakage function should beproportional to the square root of mill diameter.

The primary breakage distribution function is defined asthe size distribution of the progeny fragments breaking outof a given size class before they have had a chance to be re-broken. In other words, the breakage distribution function,bi,j,k for rock type k is defined as the mass fraction ofmaterial breaking out of size class j that appears in sizeclass i. The breakage distribution function can also beexpressed in cumulative form. The cumulative breakagedistribution function, Bi,j,k is the mass fraction of progenyparticles originating in size class j that are smaller than x[mm]. Note that xi is the upper size limit of particles in sizeclass i and the subscript i runs from a value of 1 for the

largest particles to a value n for particles in the smallest sizeclass with sizes ranging from zero to xn. If the millresidence time distribution can be modelled as a simplefully mixed reactor, the following population balanceequation can be used to keep track of the holdup mass ofparticles of given rock type k and size class i inside themill:

accumulation = flow in–flow out–consumption + generation

[2]

where wi,k is the holdup mass of size class i and rock type kparticles, [t]fi,k is the mill inlet flow rate of size class i and rock type kparticles, [t/h]pi,k is the discharge flow rate of size class i and rock typek particles, [t/h]t is time, [h]This formulation of the standard SAG model follows the

one available in the MinOOcad dynamic simulationpackage (Herbst and Pate, 2001). In this version of themodel, the discharge flowrate is expressed as the product ofthe holdups and the so called specific discharge ratefunction, gi,k [h]-1:

[3]

After substituting this value for pi,k, Equation [2] (for allvalues of i and k) takes the standard form of a state variabledescription of a lumped dynamical system (Athans,Dertouzos, Spann, and Mason, 1974). The dependentvariables or states are given by the holdups, wi,k inside themill. The independent variable is the time, t. Measurableoutputs, which include discharge flows, the net power, andthe ore mass holdup are all functions of the state variables.The resulting set of differential equations can be solvednumerically to simulate both the dynamic and steady statebehaviour of the mill.

In principle, it should be possible to measure the specificbreakage rate and breakage distribution functions directlyfrom pilot-scale SAG batch tests using radioactive tracertechniques to ‘tag-and-track’ parent and progeny fragments

Figure 3. Modifications of grate discharge total opening area



in the mill. However, the technological challenges of doingthis are immense and have yet to be addressed. To getaround this problem, it is usually assumed that the breakagerate and breakage distribution functions can be expressed interms of simple analytical equations with a minimal numberof parameters. In principle, these parameters can be back-calculated from operating data by statistical methodsinvolving the minimization of weighted sums of squares(Austin, Klimpel, and Luckie, 1984).

Unfortunately, there appears to be very little consensusamongst researchers with regard to the best choice for themathematical structure of the specific breakage rate andbreakage distribution functions. This is understandable ifone recognizes that in a SAG mill (unlike a conventionalball mill) there is no clear distinction between the particlesdoing the grinding (pebbles, rocks, and balls), and theparticles being ground. It has been argued (Sepúlveda,2001) that the effectiveness of the balls as grinding mediashould be proportional to the power drawn from them.Similarly, one would expect the effectiveness of the pebblesand rocks as grinding media to be proportional to the powerthey draw. It follows that the formulation of a rigorouspopulation balance model with a clearly-defined specificbreakage rate and breakage distribution functions becomesvery complex. Suffice to say, some schools of thoughtprefer not to factor out a specific power component whenformulating a population balance model (Austin, Menacho,and Pearcy, 1987).

There are also differences of opinion with regard to thedefinitions of breakage and distribution functions. Mostresearchers treat breakage as a continuous processinvolving a statistical average of a very large number ofbreakage events with particles breaking into and out of agiven size class. In this case the element, bi,i,k of thebreakage distribution function has a value of zero bydefinition. On the other hand, some researchers viewbreakage as a sequence of discrete events and makeallowance for particles breaking in a given size class toproduce progeny fragments that appear in the same sizeclass. In this case the element, bi,i,k can then take on positivenon-zero values (Lynch, 1977).

Consideration will now be given to some of the optionsfor ‘fixing’ the breakage distribution and breakage ratefunctions in the standard model.

Fixing the primary breakage distribution function It is generally conceded that the main modes of breakage inSAG mills are abrasion, impact fracture, and attrition.

It has been argued that abrasion grinding is the dominantmode of breakage in AG/SAG mills (Loveday, 2004),which can be defined as the process whereby ore pieces arerubbed against each other and gradually get worn downuntil they are small enough to be caught between the largerpieces.

Impact fracture has two causes, either the blow of theprotruding parts of the mill liner against the ore pieces inthe charge or the impact caused by flying balls or pebbleswhen hitting the charge or the shell liner. The first causeoperates at both cascading and cataracting speeds, thesecond only at cataracting speeds.

Attrition grinding is the usual term for comminutioncarried out by the action of the grinding media as balls orpebbles on the interstitial fine material.

It should be evident that the breakage distributionfunction should be structured to cater for all the modes ofbreakage described above.

One approach to the dilemma of getting an estimate ofthe breakage distribution function is to postulate a plausiblebreakage distribution function from laboratory tests usingrocks or particles in narrow size ranges (Napier Munn,Morrell, Morrison, and Kojovic, 1996). These tests includesimple batch tumbling tests (Austin, Menacho, and Pearcy,1987) to provide an estimate of the abrasion component ofthe breakage distribution function and dropweight tests(Pau and Maré, 1988) on single rocks to get the impactfracture component. It turns out that the size distribution ofthe products of breakage for both abrasion and impact canbe correlated in terms of either a truncated Rosin Rammlerdistribution or a weighted sum of two truncated RosinRammler distributions (Austin, 1993). The truncated RosinRammler distribution is given by the equation:

[4]

PTi is the mass fraction less than size xi and dmax is the

truncation or maximum particle size. The parameters a andm determine the shape of the size distribution plot. Theslope of the size distribution on a log-log scale at fine sizesis determined by m. The parameter a can take on eitherpositive or negative values. Negative values for a can beused to approximate impact size distributions at low energyinputs and positive values can be used to simulate highenergy impacts. In the limit as a → 0, Equation [4] becomesa Schuhmann distribution, which plots as a straight line ona log-log scale.

Figure 4 shows a ‘fabricated’ estimate of an energy-dependent cumulative breakage distribution function for a1.7 m diameter pilot SAG mill based on laboratorydropweight and tumbling tests. Many simplifyingassumptions were made in the formulation of this function.These included: allowance for size-dependent effects on thedistribution of specific energy inputs inside the mill,normalization of the impact breakage distribution withrespect to top size for a given specific energy input, and theweighting of the impact and abrasion components toprovide the overall breakage distribution function. Given,also, that the tests used to generate this breakagedistribution function did not cater for attrition modes ofbreakage, there is considerable doubt whether the estimatedfunction reflects reality and one would have got the sameresult from an idealized ‘tag and track’ test using acontinuously fed mill and a complete spectrum of ROMsizes. However, if the breakage distribution function isfixed, only the parameters of the specific breakage ratefunction need to be back-calculated from subsequent testsconducted on the pilot or production mill.

Fixing the specific breakage rate functionIn common with the breakage distribution function, it isusual to assume that the specific breakage rates can beexpressed in terms of an analytical equation. Such anequation (Austin, Menacho, and Pearcy, 1987) is given by:

[5]

where �1,k, �2,k, �1,k, �2,k, �k, and �k are parameters thatmust be estimated by back-calculation. Particle size is



usually expressed in terms of the geometric mean size for agiven size class, xi [mm]. The first term on the right-hand-side attempts to account for both attrition breakage at finesizes and abrasion breakage at intermediate sizes. Thesecond term accounts for the effects of self-fracture, whichbecomes dominant at coarse rock sizes (typically above100 mm). Figure 5 shows what this function looks like whenplotted on a log-log scale and the effect of varying one ofthe parameters (�k). Needless to say, the estimation of allthese parameters by back-calculation with a reasonable levelof precision and statistical confidence is a challenging taskfor a single set of conditions, let alone for a wide range ofoperating variables and mill liner/grate geometries.

The specific discharge rate functionFor SAG mills with high aspect ratios (D⁄L > 2), it isgenerally acknowledged that the mill charge is fully mixed.In this case, the specific discharge rate function can bedefined as the ratio of the discharge flowrate of a given

rock type and size interval to the hold-up of the same rocktype and size interval inside the mill. This function can beuniquely estimated from measurements of size distributionsand mass flows of the feed and discharge streams togetherwith the size distribution and hold-up mass of the millcharge. The size distribution and composition of the millcharge can easily be measured at pilot scale, but this canbecome a formidable task at production scale. Even at pilotscale, the estimation of the specific discharge rates can besensitive to small measurement errors. This is especiallytrue for the case where the size distribution of the millcontents is bimodal and close to being gap graded, which isoften the case. In the ‘gap’ region, the specific dischargefunction is expressed as the ratio of two numbers close tozero, which can give rise to a large variance for theestimated specific discharge rates.

Because of the practical difficulties of measuring specificdischarge rates in production mills, it is common to assumethe specific discharge rate can be expressed as an analytical

Figure 4. Cumulative breakage distribution function for standard SAG model

ˆ

Figure 5. Specific breakage rate function for a pilot SAG mill



function. For a grate with pebble ports, it is believed thatthe specific discharge function takes the form (Napier-Munn, Morrell, Morrison, and Kojovic, 1996) given by:

[6]

In this equation (shown graphically in Figure 6), it isassumed that the specific discharge rates for particles up tosize xm (about 1 mm) are constant with a value dmax [h]-1.Above this size the specific discharge rate decreasesmonotonically with increasing particle with a change inslope at the mesh size, of the grate apertures, xg [mm], andhas a value of zero at the mesh size of the pebble ports,xp [mm]. The parameter fp relates to the relative open areasof the grate apertures and pebble ports. Back-calculatedestimates of the specific discharge function based on thisequation have been reported in the literature (Mainza,Powell, and Morrison, R D, 2006).

A simplified model for SAG milling

Concept of a cumulative breakage rate functionThe concept of using a single function to describe breakagekinetics for conventional grinding mills (ball, rod, andpebble mills) is not new (Hinde, and King, 1978), (Finchand Ramirez-Castro, 1981), and (Austin, Klimpel, andLuckie, 1984). The application of the concept of acumulative breakage rate function to the steady statemodelling of a SAG mill was described in 1993 (Austin,Sutherland, and Gottlieb, 1992). The dynamic modelling ofan open circuit mill SAG mill using this concept wasdescribed in 1993 (Amestica, Gonzalez, Barria, Magne,Menacho, and Castro, 1993) and again in 1996 (Amestica,Gonzalez, Menacho, and Barria, 1996).

The specific cumulative breakage rate function, Ki,k [h]-1

is defined as the fractional rate at which particles of a givenrock type, k above a given size, xi in the mill break to belowthat size per unit time. In common with the approachadopted for the standard model (Equation [2]), atransformation relationship is used to define an energybased cumulative breakage rate function,

KEi,k [kWh/t]-1 (KE

i,k = (M⁄P)Ki,k). Consider the fractional rates at which particles above

sizes xi and xi+1 break to below these sizes, as indicated inFigure 7. Let the total or cumulative masses above thesesizes inside the mill be Wi and Wi+1, respectively. If the millis operated in a simple batch mode the rate of change ofmass for particles in size class i and rock type k is given by:accumulation = consumption above size xi – consumption

above size xx+1

[7]

It follows that a single function can be used to uniquelyquantify breakage kinetics in a SAG mill and to establish amass balance for material within a given size class.

Formulation of the cumulative rates population balancemodelConsider a population balance for a continuously-fed millfor particles in size class 1 (whose upper mesh size is equalto or greater than the largest particle in the feed) and rocktype k. If there are no particles coarser than size x1 thespecific breakage rate of particles coarser than this size, KE

1,k

is undefined. It follows that the population balance equationwith respect to time for size class 1 is given by:

accumulation = in – out – consumption

[8]

where F2,k and P2,k are the cumulative mass flows ofmaterial coarser than size x2 in the feed and productstreams, respectively. For the first size class, Equation [8] isidentical to:

Figure 6. Specific discharge rate function for SAG mill with pebble ports



accumulation = in – out – consumption

[9]

The first term on the right-hand side of Equation [9] givesthe flowrate of size class 1 and rock type k into the mill.The second term expresses the discharge flow rate in termsof the value of the specific discharge function and massholdup for size class 1 and rock type k. The third term inEquation [9] assumes that breakage rates are proportional tothe product of the specific power input and the mass of sizeclass 1 material inside the mill. When expressed in thisform, the energy-based specific breakage rate function, KE

i,k[kWh/t]-1 is assumed to be insensitive to scale-up. It shouldbe noted that the power draw of the mill is stronglydependent on the hold-up of rock and pebbles inside themill, which makes it necessary to solve this equation bynumerical methods.

The accumulation or rate of change of the hold-up ofmaterial coarser than xi (i = 2,3�, n – 1) is given by:

[10]

where the first term on the right-hand-side of this equationis the inlet flowrate of rock type k coarser than size xi andthe second term is the discharge flowrate of materialcoarser than size xi. The third term is the rate at whichmaterial coarser than size xi breaks to below this size. Asimilar equation can be applied to material coarser than sizexi+1:

[11]

Subtracting Equation [10] from Equation [11] gives theaccumulation of material within size class i:

accumulation = in – out + (generation – consumption)

[12]

The mass balance for particles in size class n (the sinkinterval with particle sizes between zero and xn) is given by:

[13]

The water balance is given by:

accumulation = in – out + [14]

The above equations can be solved numerically to simulateboth the dynamic and steady state behaviour of the mill forany circuit configuration.

The total mass of ore inside the mill is obviously afunction of the hold-ups of particles of all rock types and allsizes. The power is a function of the hold-ups of water, ore,and grinding media. A number of model equations areavailable in the literature for predicting the power draw,such as the one developed for SAG mills given in Equation[15] (Austin, 1990):

[15]

where J and JB are the static fractional volumetric filling ofthe mill for the total charge and for the balls, respectively.The effective porosity of the charge is given by �c and wc isthe weight of the ore expressed as a fraction of the totalmass of ore and water in the mill. The density of the ballsand average density of the ore [t/m3] are given by �B and �r,respectively, and c is the mill speed expressed as afraction of the critical speed.

Figure 7. Concept of a cumulative breakage rate function

ˆ



The Mintek version of the cumulative rates modeldescribed above caters for the effects of different aspectratios (D⁄L) when scaling up pilot data by treating theproduction mill as a number of fully-mixed reactors inseries with back mixing between adjacent reactors.

Measuring the cumulative breakage rate functionIt can be shown from the population balance equations forthe solids given above (Equations [9], [12], and [13]) thatthe cumulative specific breakage rate function can beobtained directly from plant data. By definition, there areno particles coarser than x1, KE

1,k so is undefined. Thespecific breakage rates for particles coarser than size x2(particles in size class 1 only) can be obtained at steadystate by equating the derivative in Equation [9] to zero andrearranging terms:

[16]

After equating the derivatives to zero in Equation [12],values for the cumulative breakage rate function can becalculated recursively for i = 2,3,...,(n -1):

[17]

From Equation [13] (for i = n):

[18]

In a pilot mill, all the terms on the right-hand-side of theabove equations are directly measurable.

Bench scale SAG testworkBench-scale SAG testwork followed by computersimulation studies are becoming a common feature fordesigning milling circuits at prefeasibility studies stage.Bench-scale comminution testwork used to designAG/SAG mills include Bond ball work index (BBWI),Bond rod work index (BRWI), JKTech drop weight andabrasion tests, SAG Mill comminution test (SMC), SAGpower index (SPI), Advanced media competency test(AMCT), McPherson autogenous test and SAG design test.Table I shows a summary of bench-scale testworkequipment used, requirements in terms of mass of sample,top size used and outputs.

These bench-scale testwork have been extensively

discussed at the 2006 Autogenous and Semitogenousconference (Starkey, J. et al, 2006; Morrel, S., 2006;McKen, A. and Williams, S., 2006). Assumptions are madeto derive parameters like in the JK drop weight test whereinitially it was assumed that the drop weight test productsize distribution for rock of different size obtained at aspecific energy input can be normalized. Figure 8 illustratesthat the product size distribution cannot be normalized for aUG2 ore.

Mintek SAG testworkMintek has been actively involved for many years inresearch in order to improve laboratory test procedures forthe design and optimization of SAG mills. Motivated by theneed:

• to reduce the amount of sample used for piloting testswhile not compromizing on the quality of datagenerated

• to reduce assumption made in analysing the datagenerated

• to design a test not relying on a database to interpret theresults

Mintek has designed a test to take into account the above-mentioned criteria.

Mintek SAG testwork is conducted in a 0.6 m diametermill using feed with a top size of 75 mm. The design of themill was performed to have the same flexibility as the pilotmill. The variable speed drive mill is equipped with gratedischarge which can be modified as illustrated in Figure 9.

The mill can run as a fully autogenous or semi-autogenous with top ball size of 80 mm. The mill isequipped with instrumentation for monitoring shaft torqueand mill speed, which is linked to a data-logging computer.The net power can therefore be calculated.

Dry looked cycle tests are conducted in dry conditions aslocked-cycle until steady state conditions are achieved.Different configurations can be used. The mill dischargecan be screened and oversizes sent back to the mill.

At the end of a test, the mill content is weighted, analysedfor build-up of a critical size or rock type and sized. Themill discharge is also weighted and sized. The mill productcan be used for Bond ball work index testwork.

The sample required to conduct the Mintek SAG test isapproximately 300 kg with a top size of 75 mm to exploredifferent conditions.

Comparison between piloting data and Mintek SAG testdata on a UG2 orePiloting testwork were conducted using a UG2 ore in aconfiguration shown in Figure 10. The mill was loaded at30% filling with a ball charge of 6%. The mill discharge

Table ISAG bench-scale testwork

Testwork Equipment Mass of Top size Outputsample (kg) (mm)

JKTech drop weight test Drop weight tester 80 63 A, b, ta SAG Mill Comminution test (SMC) Drop weight test 20 31.5 DWI, AxbMinnovEX SAG Power Index (SPI) Mill having a diameter of 0.3 m 10 19 Specific energy required (kWh/t)Advanced Media Competency Test (AMCT) Mill having a diameter 300 165 Pebble competencyMacPherson Autogenous Mill having a diameter of 0.46 m 175 32 Specific energy required (kWh/t) and

MacPherson autogenous work index (AWI)SAG design test Mill having a diameter of 0.5 m 20 32 Specific energy consumption



Figure 8. Normalized drop weight size distribution

Figure 9. Example of grate discharge used on the Mintek laboratory SAG mill



was screened at 1.7 mm. The oversize was recirculated tothe mill and the undersize was the final product. The feedrate to the mill was 1.67 t/h to maintain a constant charge inthe mill of 30% filling.

After 8 hours, when the mill was running at steady-state,samples were taken for mass balance. The mill content wasalso sized after a crash stop.

Mintek laboratory SAG testwork was conducted underthe same conditions as the piloting testwork. Locked-cycletests were conducted using the same configuration. Batchgrinding were conducted for 5 minutes. The discharge ofthe mill was screened at 1.7 mm and the oversizerecirculated to the mill. Fresh feed was added to the millaccording to the feed size distribution to maintain aconstant charge in the mill. The process was repeated untilsteady-state condition was achieved in 11 cycles.

A comparisons in terms of specific energy consumed isshown in Table II. It can be seen that the laboratory MintekSAG test predict within an accuracy of 5%.

The comparison between the specific discharge rate andthe cumulative specific breakage rate are illustrated

respectively in Figures 11 and 12. The large differences in the specific discharge rate

observed below 1 mm is due to the loss in the dust since thetest is conducted in dry conditions.

The test facility is currently being modified to reduce dustlosses to acceptable levels.

ConclusionsMintek is equipped with comminution piloting facilitieswhich can be used for the design and optimization ofAG/SAG mills.

The breakage processes occurring in SAG mills arecomplex and any proposed simulation model is going to bean approximation to the actual behaviour of the mills. Theconcept and application of specific breakage rate andprimary breakage distribution functions have been veryuseful in describing the effects of ball load, ball size andother variables on the performance of conventionaltumbling ball mills. It is therefore natural to extrapolate thisinformation to SAG mills. This paper has endeavoured tohighlight some of the unresolved issues associated withpopulation balance models for SAG mills that requireseparate breakage rate and breakage distribution functionsto quantify breakage phenomenon. The major dilemma withthis approach to SAG modelling is that these functionscannot easily be measured and there is much doubt as towhether or not the values obtained are reproducible andaccurately reflect reality. Even if they could be measureddirectly, it still remains a formidable task to establish how

Figure 10. Piloting circuit used for the grinding of UG2 ore

Table IIComparison between specific energy used

Net power (kW) Feed rate (t/h) Specific energy(kWh/t)

Pilot test 8.7 1.67 5.20Mintek SAG test 0.432 0.087 4.96

Figure 11. Comparison between the specific discharge rate



these functions change with operating conditions inside themill and the geometry of liners and grates.

To address the problems associated with the standardapproach to modelling SAG mills, a much simpler modelstructure is proposed which requires fewer assumptions,and where functions describing breakage kinetics andmaterial flow through the discharge grate can be measureddirectly. However, the ‘simple model’ does require thedevelopment of a set of empirical relations to cover theeffect of all variables on the KE

i,k and gi,k functionscharacterizing breakage behaviour and material transport inand around the mill. Nonetheless, it is believed that this is avery valid approach and may turn out to be the quickestway to fully describe and quantify the performance of thesecomplex mills.

Comminution bench scale laboratory testwork followedby computer simulations are becoming a growing practiceto design AG/SAG circuits since piloting tests require morethan 80 tons of samples and the cost is very high. This hasprompted Mintek to develop a laboratory test procedurethat obviates the need for databases by providing estimatesof breakage and discharge rate functions that can be useddirectly to predict the performance of production circuits.

The test developed is conducted in a variable speed andgrate discharge laboratory grindmill having a diameter of0.6 m equipped with torque and speed measurement whichare linked to a computer logging system. The test isperformed as locked cycle in dry conditions. Data generatedwere compared to piloting data generated. A goodagreement has been found between the pilot data and theMintek SAG test. More tests are currently being conductedto validate the Mintek SAG test which has been filed for apatent.

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Figure 12. Comparison between the cumulative specific breakage rate



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Adrian HindeSpecialist Consultant, Mintek

Adrian Hinde is a physics graduate from Imperial College, London University where he obtained aPhD in superconductivity. He emigrated to South Africa in 1970 and worked for the Chamber ofMines Research Organisation for 21 years. His work at the Chamber covered both mining andmetallurgical activities, which included underground processing, backfilling, and instrumentationdevelopment. His first involvement with grinding operations was through the development of on-stream particle size analysers for the control of milling circuits. He joined Mintek in 1991 wherehis work has focused mainly on the design and optimisation of grinding circuits based onlaboratory and pilot test work. He holds the position of Specialist Consultant in the Minerals

Processing Division covering commercial service work as well as research and development activities. He is also involved inthe mentoring and training of young engineers and technicians.


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Pilot and laboratory test procedures for the design of